1. Field of the Invention
The invention is related to microelectromechanical systems (MEMS) and more particularly to MEMS sensors and resonators.
2. Description of the Related Art
In general, microelectromechanical systems (MEMS) are very small mechanical devices driven by electricity. Typical MEMS devices include resonators, sensors, and actuators, which may be used in various applications, e.g., accelerometers and gyroscopes. The mechanical systems of those MEMS devices may be modeled as a harmonic resonator (FIG. 1) having a natural or resonance frequency,
            ω      0        =                  k        m              ,and a quality factor,
      Q    =                            ω          0                ⁢        m            γ        ,where k is a spring constant, m is mass, and γ is a damping coefficient. The quality factor of a resonator is a dimensionless parameter that describes how under-damped an oscillator or resonator is, or equivalently, characterizes the bandwidth of the resonator relative to its center frequency. A higher Q indicates a lower rate of energy loss relative to the stored energy of the resonator, i.e., the oscillations die out more slowly. For a sinusoidally driven resonator, an increased Q corresponds to greater amplitudes of resonation, but a smaller range of frequencies around the resonant frequency for which it resonates (i.e., smaller bandwidth). Although in some applications higher selectivity (i.e., higher Q) is a critical design parameter for a MEMS device, in other applications a wider bandwidth (i.e., lower Q) is a critical design parameter.